China's only aircraft carrier entered the Taiwan Strait in a highly symbolic show of strength, but Taiwan insisted Wednesday there was no need for panic even as tensions boil over the island's diplomatic status.

Beijing has upped its military drills near the island in recent weeks after being incensed by a congratulatory phone call from Taiwan's leader Tsai Ing-wen to US President-elect Donald Trump, and by a subsequent transit stop by Tsai in the US, AFP reported.

China considers Taiwan a breakaway province to be brought back into its fold. The US is the island's most powerful ally and main arms supplier, despite having no official diplomatic relations since recognizing Beijing in 1979.

The Liaoning aircraft carrier has not entered Taiwanese waters but has gone into an area covered by the island's air defense zone, Taiwan's defense ministry said.

Beijing responded that it was "very normal" for the Liaoning to pass through an international waterway as part of drills.

"Every year, in this season, China's Navy has a few exercises in the near seas and other maritime regions. These exercises are all for training," said Liu Zhenmin, vice minister of foreign affairs.

Taiwanese media said that F-16 fighter jets and other aircraft were dispatched Tuesday night to monitor the Chinese carrier group. The Defense Ministry would not confirm those reports.

Tsai, who is currently on a visit to Central America, has been regularly instructing the national security team and the Defense Ministry by phone, presidential office spokesman Alex Huang said.

"The military is monitoring the whole situation and will act as necessary. We urge Taiwan's people to be at ease," the Defense Ministry said in a statement.

"There is no need for us to overly panic," said the chairwoman of Taiwan's Mainland Affairs Council (MAC), which handles the island's relationship with Beijing.

The Liaoning has been carrying out its first exercise in the Pacific and already passed south of Taiwan last month.

It entered the southwest of Taiwan's air defense identification zone (ADIZ) at 07:00 Wednesday local time (2300 GMT), the Defense Ministry said, along with escort vessels.

By midday it was moving north along the mainland's coast, the ministry said.

Tsai visited the US at the weekend on a transit to Central America, despite protests from Beijing.

She stopped in Houston on Saturday and met with Republican Senator Ted Cruz during her stay, which was slammed by Beijing as an attempt to "undermine China-US relations".